Solve for j j+7>3j-4

$j + 7 > 3 j - 4$

Step 1

Move all terms containing $j$ to the left side of the inequality.

Subtract $3 j$ from both sides of the inequality.

$j + 7 - 3 j > - 4$

Subtract $3 j$ from $j$ .

$- 2 j + 7 > - 4$

Step 2

Move all terms not containing $j$ to the right side of the inequality.

Subtract $7$ from both sides of the inequality.

$- 2 j > - 4 - 7$

Subtract $7$ from $- 4$ .

$- 2 j > - 11$

Step 3

Divide each term in $- 2 j > - 11$ by $- 2$ and simplify.

Divide each term in $- 2 j > - 11$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 j}{- 2} < \frac{- 11}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 j}{- 2} < \frac{- 11}{- 2}$

Divide $j$ by $1$ .

$j < \frac{- 11}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$j < \frac{11}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$j < \frac{11}{2}$

Interval Notation:

$(- \infty, \frac{11}{2})$

Solve for j j+7>3j-4

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